... class of all trees) with a given numberof independent sets It is an open conjecture [13] that all but finitely many positive integers can be represented as the numberof independent sets of some ... sizes of independent sets in graphs (see [3]), there is no distribution result known for the numberof independent sets itself yet Considering the numberof independent sets of a randomly chosen ... fortiori (Rn (0, 0) is a subset of the setof all trees in Rn whose numberof independent sets is divisible by m) with c = z0 + ǫ < z0 ˜ for suitable ǫ the electronic journal of combinatorics 16 (2009),...
... An interesting paper of Wagner [5] looks at the numberof independent sets modulo m Wagner showed that the proportion of trees on n vertices with the numberof independent sets divisible by m ... result in [1] that the Fibonacci numbers (of the paths) form a complete system of residues if and only if m = t · 5k , t = 1, 2, 4, 6, 7, 14, 3j where k 0, j The numberof matchings in a tree In this ... [3] V Linek, Bipartite graphs can have any numberof independent sets, Discrete Math 76 (1989), 131–136 [4] H Prodinger and R.F Tichy, Fibonacci numbers of graphs, Fibonacci Quart 20 (1982), 16–21...
... the electronic journal of combinatorics (1999), #R2 Abstract The asymptotic behavior of the numberofset partitions of an n-element set into blocks of distinct sizes is determined This ... values of n, we shall use elementary estimates and some well-known bounds for ordinary partitions (of a number) to express most values of bn in terms of the numberof ordinary partitions of k with ... asymptotic form of bn+1 /bn for n near m(m + 1)/2 as m → ∞ It is of interest to note that bn grows roughly like the square root of the total numberof partitions of an n element set, denoted say...
... To complete the proof it is sufficient to show that the numberof (k, )sum-free subsets of [1, n] satisfying either (1) or (2) is o(2n/ρ ) Denote by B the setof all such subsets, and let B(K, ... Sum-free sets and related sets, Combinatorica 18 (1998), 449– 459 [3] N J Calkin, On the numberof sum-free sets, Bull Lond Math Soc 22 (1990), 141–144 [4] N J Calkin, A C Taylor: Counting sets of ... natural numbers x, r let ϕr (x) be the numberof positive integers m ≤ r relatively prime to x and let ϕ(x) abbreviate ϕx (x) For a finite set A of integers A define: the electronic journal of combinatorics...
... Theorem Proof of Theorem Let A be a member of a set M = {Mi } of translates of a centrally symmetric convex set in the plane such that the clique numberof the intersection graph H(M) of M is k ... V Case yu < yv Repeating the proof of Case with roles of A and B switched yields this case The proof of Claim 3.2 is the same (with C in place of B) Proof of Claim 3.3 Let A∗ = 2A, B ∗ = A∗ ... y K Proofs of Theorems and It will be convenient to prove the following slightly refined version of Theorem for centrally symmetric sets Theorem Let M = {Mi } be a setof translates of a centrally...
... collection of convex subsets of Rd If the intersection of every d + elements of C is non-empty, then the intersection of all the elements of C is non-empty Lemma Let S be a collection of subsets of ... collection of subsets of Rd and let X be a setof points in Rd We will say that X pierces C if every C ∈ C is intersected by X For a finite collection S of sets define P (S) as the piercing numberof ... disjoint sets S1 , S2 , S3 ∈ S If A, B ∈ S are two disjoint sets, then one of these sets intersects all the sets from S \ {A, B} Proof For contradiction, suppose that there exist pairwise disjoint sets...
... Proof Lemma 2.4 Let m|n and Pm|n1 , nj (n) indicate the numberof partitions of an n -set into subsets of size m, such that in j subsets from m special elements of n the set, there exist in numbers ... m n m subsets, Hence, by using definition of multinomial coefficients, this lemma is proved ✷ Lemma 2.3 Let Pm (n) indicate the numberof partitions of an n -set to maximal numberof subsets with ... Behboodian and S M Mirhosseini of A, such that m i=1 Ai = A and Ai ∩ Aj = φ, ∀i = j The numberof partitions of a setof size n ( n -set) is called the Bell number, in honor of famous mathematician “Eric...
... approved by the Ethics Committee of the Nihon University School of Medicine and the Clinical Studies Committee of Nihon University Hospital [10] Table Characteristics of study participants Biochemical ... assess the contribution of confounders (gender, BMI) [17] A value of P < 0.05 was considered statistically significant Figure A: Nucleotide sequence of the 5’-flanking region of the human NPPB gene ... codon; Underlining, the variable numberof tandem repeat (VNTR) consists of the nucleotides (TTTC) This figure shows the 11 repeat types B: Nucleotide sequence of the 11 and 16 repeat allele Results...
... Structure of the numberof companies specified by the numberof employees Source: IT Industry Department, Ministry of Posts and Telematics of Vietnam Currently, Vietnam has around 10 software parks ... substantial numberof high-end system software, general software In the next few years, China software outsourcing industry aims to obtain the annual growth of about 50%, being far higher than that of ... According to statistics of the IT Industry Department, the US is a big software exporter but its import of software accounts for 30% of the total spending for software of the world and its payment...
... understanding of the underlying ideas of the author as well as the cultural features and social aspects of the time Like other types of story, a short story consists of five elements: - Setting is ... worthy piece of literary work often come from real life Therefore, it can be understood that literature is a tool for the reflection of life and for the expression of viewpoints of the writers ... greediness is for the sake of my students’ advantages When their teacher of English has a thorough understanding of one of the target cultures, the students would benefit Instead of being taught about...
... the Ministry of Education and Training will introduce new measures in an effort to reduce the numberof student dropouts Last school year, the numberof dropouts was lower than that of the previous ... Quach Tuan Ngoc, head of the Department of Information 11 and Technology under the Ministry of Education and Training The development and application of ICT was an essential part of reforming the ... Minister of MOET Banh Tien Long said that the ministry is now focusing on upgrading training quality by settling the problem of lack of lecturers Long said that every year, MOET will send 3% of lecturers...
... These are the reasons why I feel physical courses should be part of the graduation requirements of any university or college; they are of high value for a student’s health, character-training and ... participating in them, we can recognize the true meaning of cooperation which is defined as a situation in which rewards are distributed equally on the basis of mutual interactive behavior among individuals...
... development of New settlements in the South-West of Hanoi Figure Land use pattern of Linh Dam (Mapping - Quyen Phuong, 2011) Table Land use planning of Linh Dam (Total area: 1,840,230 m2) Types of use ... development of New settlements in the South-West of Hanoi 3.2 Linh Dam New Town - more than 10 years for a model of New Towns Due to a rapidly growing population in Hanoi, construction of new houses ... for the development of the southern gateway of Hanoi capital Since 22 - 01 - 2009, the Minister of Construction has officially signed a decision that recognized Linh Dam is one of two new urban...
... on the basis of total gas volume evolution rate and the fraction molar of the measured value of CO2 RESULTS AND DISCUSSION Temperature profiles The bed temperature profiles of each of the composting ... have been no studies of the effect of the vertical pipes on the passive aeration and the composting rate The objective of this study is to evaluate the effect of the numberof the perforated pipes, ... order to determine the effect of the numberof the ventilation pipes on the composting rate, an attempt was made to correlate the composting rate with the numberof the perforated pipes for air...
... the washout of sludge from the reactor, and therefore, we investigated the effect of surface loading rate and aeration rate on the selection of well-settling sludge and the formation of aerobic ... influencing the selection of well-settling sludge because the sludge selection is one of the most important operational strategies that are essential to successful formation of aerobic granular sludge ... strategy for the selection of well-settling sludge Then, we applied the strategy to the formation of aerobic granular sludge in a continuous experiment In addition, the effect of feeding pattern, i.e...
... hardware, and processing capacity of the DSP modules of the GWs; and Developing a script or suite for determining the numberof stages for setting up a prespecified numberof calls in multiple stages ... of dialing It measures the response time by subtracting the time of occurrence of the telephony events It then emulates playing of a setof voice prompts with pauses to accommodate play-out of ... all of the calls are made and the call setup time is sec, then successful establishment of all the connections 158 AUTOMATION OF CALL SETUP IN IP TELEPHONY FOR TESTS Figure B-5 Staggering of the...
... function of the numberof sources, Ns , is the vector of parameters needed for the model that generated the data Y The criteria are composed of the negative of the ˆ ˆ log-likelihood function of the ... both of these methods, the estimate of the numberof sources is that value of Ns which minimizes the criterion In [9] there is a more thorough discussion concerning determining the numberof degrees ... than sensors, then the rank of SCS is equal to the numberof signals incident on the array or, equivalently, the numberof sources If there are Ns sources, then SCS is of rank Ns and its Ns eigenvalues...
... A2, , Am, each of which associated with a fuzzy subset over the setof alternatives X = [X1, X2, , Xn], the decision function D(x) can be denoted, in terms of fuzzy subsets, as [Yager 1978] ... can be a combination of p decision rules, and the possible numberof these combinations, n, depends on the numberof rules at each level or decision point A combination of scheduling rules can ... combination of rules is one of the possible combinations of rules If three rules are assumed for each decision point, the number p of possible combinations would be Each combination of rules,...
... Gδ -subset of X A subset Y ⊂ X is called a Gδ -set (in X) if Y is a countable intersection of open subsets of X Its complement X \ Y is called an Fσ -set We remark that no irrational number λ ... Cantor setof nonergodic directions We begin with the proof of Lemma 1.1, which is the recipe for the construction of a Cantor set E(λ) ⊂ K(λ) We then show that the Hausdorff dimension of E(λ) ... in P , then Po is a residual subset (i.e., contains a dense Gδ -subset) of P In particular, Po is uncountable if P is Proof Since the family of residual subsets of P is closed under countable...